1. Field of the Invention
The present invention generally relates to the area of computer aided engineering analysis, more particularly to method and system for transferring state variables between an old and a new model in an adaptive mesh-free analysis.
2. Description of the Related Art
Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems relating to complex systems since its invention in late 1950's. With the advent of the modern digital computer, FEA has been implemented as FEA computer program product. Basically, the FEA computer program product is provided with a model of the geometric description and the associated material properties at certain points within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The individual elements are connected together by a topological map, which is usually called mesh. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings.
Although FEA has been successfully applied to many fields to simulate various engineering problems, there are some instances that FEA may not be advantageous due to numerical compatibility condition is not the same as the physical compatibility condition of a continuum. For example, in Lagrangian type of computations, one may experience mesh distortion, which can either end the simulation prematurely or result in drastic deterioration of accuracy. In addition, the FEA often requires a very fine mesh in problems with high gradients or a distinct local character, which can be computationally expensive. For this reason, adaptive FEA has been developed to allow the FEA mesh be regenerated after certain number of solution cycles, such that the original mesh can be refined in the region experiencing high distortion.
Adaptive re-meshing procedures for simulations of impact/penetration problems, explosion/fragmentation problems, flow pass obstacles, and fluid-structure interaction problems etc., have become formidable tasks to undertake. The difficulties here are not only re-meshing procedure, but also mapping the values of state variables from the old model to the new model. Many ad hoc techniques such as smoothing have used for the process of transferring state variables. The problem associated with these ad hoc techniques is that the accuracy and convergence properties can not be preserved from one mesh or model to the next. As a result, inconsistent analysis results are produced.
Another method called “mesh-free analysis” has become one of the focused research topics during the 1990's. Many applications of using mesh-free analysis have been achieved in the past decade. In comparison with conventional finite element methods, the characteristics of smoothness and naturally conforming of the approximation, exemption from meshing, and higher convergence rate and the easy of nodal insertion and deletion have make mesh-free methods attractive alternative numerical techniques for nonlinear analysis of industrial applications. In a highly non-linear structural analysis, a mesh-free model can be regenerated after the error indicator exceeds a pre-determined level. Since there is no mesh, the generation of a new model is relatively easier comparing to that of the finite element analysis. Similar to the finite element analysis, the state variables need to be transferred between the old and the new models with preservation of accuracy and convergence properties. Therefore, it would be desirable to have a consistent means to transferring state variables between an old and a new model in an adaptive mesh-free analysis.